Msgr. Thomas Green, Stephan Kuttner Distinguished Professor of Canon Law, and Kurt Martens, professor, canon law, were quoted in an Atlantic story on Pope Francis saying he’s open to the possibility of ordaining married men as priests. See below.

Will Pope Francis Allow Married Men to Become Priests?

... While Francis’s comments might seem like a sign that he’s further liberalizing the traditions of the Church, Martens said this was “absolutely not” the case. “I’m surprised that after four years of Pope Francis, we are not used to what he says and how to read what he says,” Martens said. “Remember the ‘Who am I to judge?’ comment [on homosexuality]? Everyone thought he was changing Church teaching. But he was just paraphrasing in his own words the Church teaching.”

Married men can already serve a number of roles in the Church. For roughly five decades, they have been allowed to serve as deacons—leaders who preach, conduct weddings and funerals, and perform baptisms. In Eastern rite Catholic churches, priests can be married, as can Anglican priests who convert but were married before they became Catholic. Francis has often commented that he’s open to studying new forms of leadership in the Church; in May, for example, he said he was open to looking at the possibility of women deacons.

In general, though, Catholic priests remain celibate according to the traditions of the Church. “Celibacy is what you’d call a disciplinary norm,” Martens said. Unlike the question of women serving in the priesthood, he added, priestly celibacy is not a matter of dogma. Thomas Green, another professor of canon law at Catholic University, noted that while celibacy is “a strong part of the Latin tradition,” meaning the Catholic Church in the West, “it really wasn’t concrete until around the late 1100s and 1200s.” ...

Msgr. Stephen Rossetti, clinical associate professor, theology, was quoted in a Washington Post story on Pope Francis saying he is open to the possibility of ordaining married men as priests.
See below.

Pope Francis suggests an openness to ordaining married men as priests

... "The pope’s comment gives the impression that he’s not talking about Western Europe, where there is less of a clergy shortage, said Monsignor Stephen Rossetti, a Catholic University of America professor who has written books on psychological care for priests.

“He’s not saying we’re doing it, but he’s saying let’s run it up the flagpole and see what people think,” Rossetti said. “He’s saying he’s willing to make exceptions as a merciful gesture.” ...